A candy bar that originally sold for $.60 undergoes a 3% price increase each year.

Answer: sin²∅

Explanation: If you divide each term by sin squared theta, sin²∅/sin²∅ = 1, cos²∅/sin²∅ = cot²∅, and 1/sin²∅ = csc²∅, which is your result.

Answer:

sin²θ

Step-by-step explanation:

To determine what we need to divide  \(\sin^2 \theta+\cos^2 \theta=1\)  by to yield \(1+\cot^2 \theta=\csc^2\theta\),  compare equations:

\(\textsf{Equation 1}: \quad \sin^2 \theta+\cos^2 \theta=1\)

\(\textsf{Equation 2}: \quad 1+\cot^2 \theta=\csc^2\theta\)

If we divide a term by itself, it will always yield 1.

Therefore, divide each term in the first equation by sin²θ:

\(\implies \dfrac{\sin^2 \theta}{\sin^2 \theta}+\dfrac{\cos^2 \theta}{\sin^2 \theta}=\dfrac{1}{\sin^2 \theta}\)

\(\implies 1+\dfrac{\cos^2 \theta}{\sin^2 \theta}=\dfrac{1}{\sin^2 \theta}\)

\(\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}\\\\\csc \theta=\dfrac{1}{\sin \theta}$\\\end{minipage}}\)

Use the trigonometric identities for cot and cosec:

\(\implies 1+\dfrac{\cos^2 \theta}{\sin^2 \theta}=\dfrac{1}{\sin^2 \theta}\)

\(\implies 1+\left(\dfrac{\cos \theta}{\sin \theta}\right)^2=\left(\dfrac{1}{\sin \theta}\right)^2\)

\(\implies 1+(\cot \theta)^2=(\csc \theta)^2\)

\(\implies 1+\cot^2 \theta=\csc^2 \theta\)

Thus proving that sin²θ + cos²θ = 1 should be divided by sin²θ to yield

1 + cot²θ = csc²θ.

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Answer:

168 inches which is also 14 feet

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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The high temperatures in City B are more spread out than the high temperatures in City A.

The difference between the means of the two cities is 12 degrees Fahrenheit. This is equivalent to about 4 mean absolute deviations in City A or 5 mean absolute deviations in City B. This means that the high temperatures in City B are more spread out than the high temperatures in City A.

To put it another way, the high temperatures in City A are more likely to be close to the mean, while the high temperatures in City B are more likely to be further away from the mean.

Here is a table summarizing the data:

City Mean high temperature Mean absolute deviation

City A 59°F                             3.2°F

City B 71°F                                     2.9°F

The high temperatures for City A are more tightly clustered around the mean, while the high temperatures for City B are more spread out.

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

Answer:

\(sum \: of \: exterir \: anges \: for \: a \: polygon = 360 \\ 5x - 5 + x + 4x - 5 + 4x + 20 = 360 \\ x \: terms \: togather \\ 5x + x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 360 - 10 \\ 14x = 350 \\ x = \frac{350}{14} = 25 \\ x = 25 \\ thank \: you\)

Answer:

SUM OF EXTERIOR ANGLES=360

Step-by-step explanation:

5x-5+4x-5+4x+20+x=360

14x+10=360

14x=350

x=350/14

x=25

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

9 nickels, 8 dimes

Step-by-step explanation:

Let n = number of nickels, and let

d = number of dimes.

n + d = 17--------->.05n + .05d = .85

.05n + .10d = 1.25---->.05n + .10d = 1.25

------------------------

.05d = .40

d = 8, n = 9

The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.

To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:

\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)

Where:

a= 44cm

height= 44²-22²= 38.1cm

Area= 44²+ 2(44) × √44²/4 + 38.1²

= 1936+88 × √ 484+1452

= 2024× √1936

= 5807.61 cm².

Therefore the closest estimate to the final answer would be 5289.25 cm squared

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Answer:

A = $446,068.00

Step-by-step explanation:

A = $446,068.00

I = A - P = $88,068.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 8.2%/100 = 0.082 per year.

Solving our equation:

A = 358000(1 + (0.082 × 3)) = 446068

A = $446,068.00

The total amount accrued, principal plus interest, from simple interest on a principal of $358,000.00 at a rate of 8.2% per year for 3 years is $446,068.00.

The domain of the function is:

D: {x ∈ R | x ≥ -6}

Here we have:

\(f(x) = \sqrt{(1/3)*x + 2}\)

Remember that the argument of a square root can be only numbers equal to or larger than zero, so the domain of that function is such that:

\((1/3)*x + 2 \geq 0\)

Now we can solve that for x.

\((1/3)*x + 2 \geq 0\\(1/3)*x \geq -2\\\\x \geq -2*(3/1)\\\\x \geq -6\)

So the domain of the function is:

D: {x ∈ R | x ≥ -6}

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Answer:

The domain of the function is:

D: {x ∈ R | x ≥ -6}

The probability that they both get a red apple is, 15/28

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of Ed's friend grabbing a red apple is,

= 6 red apples / (2 green apples + 6 red apples)

= 6/8

= 3/4.

Then, the probability of Ed grabbing a red apple from the remaining apples is,

= 5 red apples / (2 green apples + 5 red apples)

= 5/7.

So, the probability that both Ed and his friend get a red apple is,

= 3/4 x 5/7

= 15/28

Hence, the probability is 15/28

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Answer:

15 dollars

Step-by-step explanation:

Since a shirt is an unknown cost, and the pants costs 18 dollars, they costed 33 dollars overall.

In order to find the shirt price, let's subtract the price of the jeans from the total price.

33-18=15

The shirt's price is 15 dollars.

Answer:

$15

Step-by-step explanation:

$33- total cost

-$18- pants cost

=$15 for the shirt cost

In other words 33-18=x

                            15=x

x being the cost of the shirt!

I hope this helped!

Answer:

x = 95/3

Step-by-step explanation:

3x - 7 = 88

=> 3x = 88 + 7

=> 3x = 95

=> x = 95/3

Therefore x ≠ 3, x = 95/3

Answer:

C.  y=-(2)^x + 3

Answer:

Huh? what do you mean?

Step-by-step explanation:

Answer:

y = - \(\frac{1}{12}\) x + \(\frac{127}{12}\)

Step-by-step explanation:

y = 12x - 9

Slope of line perpendicular to given is m = - \(\frac{1}{12}\)

P(7, 10)

y - 10 = - \(\frac{1}{12}\) (x - 7)

y = - \(\frac{1}{12}\) x + \(\frac{127}{12}\)

An equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9 is y - 10 = -1/12(x-7)

The equation of a line in point-slope form is expressed as;

y - y0 = m(x-x0)

Given the equation of a line y = 12x - 9

Substitute m = -1/12 and ()7, 10) into the equation above to have;

y - 10 = -1/12(x-7)

Hence an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9 is y - 10 = -1/12(x-7)

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The correct answer is U - II = I + III + IV.

In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

c represent the compliment of the particular state.

U is the union set

∩ represent intersection between the neighbouring sets

Therefore,

Bc = U - B = I + II

Bc∩A = Area common in Bc and A = II

(Bc∩A)c = Area in U but not in (Bc∩A) = U - II = I + III + IV

So, answer is d.

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The exact value of the specified trigonometric identity found using the the trigonometric identity for tan(A - B) and tan(arccos(x)) and tanarcsin(x)) is presented as follows;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

A trigonometric identity is an equality that involves trigonometric functions that is valid for all values of the arguments of the equation

The required trigonometric identities are;

\(tan (A - B) = \dfrac{tan(A) -tan(B)}{1-tan(A)\cdot tan(B)}\)

\(tan(sin^{-1}(x)) = \dfrac{x}{\sqrt{1-x^2} }\)

\(tan(cos^{-1}(x)) = \dfrac{\sqrt{1-x^2}}{x }\)

Therefore;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) = \dfrac{tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)-tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}{1-tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)\times tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}\)

Which gives;

\(\dfrac{\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } -\dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} } }{1+\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } \times \dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} }}=\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }\)

\(\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }=\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Which indicates that we have;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

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Answer: \(y=-\frac{2}{5}x+12\)

y = mx + b

m = slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}\)

The y-intercept(b) can be found by substituting a point into the function.

\(y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12\)

Therefore, the function is:

\(y=-\frac{2}{5}x+12\)

Answer:

-1519 4/5

-1519.8

-7599/5

Step-by-step explanation:

In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Row echelon form suggests that: Each row's leading (first) entry must be

Each following row's first entry must be on a new column to the right.

All rows with zero entries are listed below rows with non-zero items.

If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.

According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

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Answer:There is a negative relationship between the price level and the total quantity of goods and services demanded, all other things unchanged. The negative slope of the aggregate demand curve suggests that it behaves in the same manner as an ordinary demand curve.

Answer:

2x + y = -4

Step-by-step explanation:

standard form of equation of straight line is

ax+by = c

that  is terms containing x and y should be  on LHS and constant term should be  on RHS

______________________________________________

Given equation

y + 1 = - 2x - 3

lets bring -2x on LHS ,

add 2x on lHS and RHS

y + 1  + 2x = - 2x - 3 + 2x

=> y + 1  + 2x = -3

on lHS, 1 is there which constant term lets bring it on RHS

subtract 1 from both sides

y + 1  + 2x  - 1= -3 -1

y + 2x = -4

rearranging it

2x + y = -4  (Answer)